Theorem ancld 308

Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 1-Nov-2012.)

Hypothesis

Ref	Expression
ancld.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
ancld	⊢ (φ → (ψ → (ψ ∧ χ)))

Proof of Theorem ancld

Step	Hyp	Ref	Expression
1		idd 21	. 2 ⊢ (φ → (ψ → ψ))
2		ancld.1	. 2 ⊢ (φ → (ψ → χ))
3	1, 2	jcad 291	1 ⊢ (φ → (ψ → (ψ ∧ χ)))

Syntax hints:   → wi 4   ∧ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101

This theorem is referenced by:  mopick2  1980  cgsexg  2583  cgsex2g  2584  cgsex4g  2585  reximdva0m  3230  difsn  3492  preq12b  3532  elres  4589  relssres  4591  fnoprabg  5544  1idprl  6564  1idpru  6565  msqge0  7360  mulge0  7363  fzospliti  8762